scholarly journals Verifying Heisenberg’s error-disturbance relation using a single trapped ion

2016 ◽  
Vol 2 (10) ◽  
pp. e1600578 ◽  
Author(s):  
Fei Zhou ◽  
Leilei Yan ◽  
Shijie Gong ◽  
Zhihao Ma ◽  
Jiuzhou He ◽  
...  
Keyword(s):  
Quantum Physics ◽  
Uncertainty Relations ◽  
Independent Manner ◽  
Trade Off ◽  
Single Spin ◽  
Spin Level ◽  
Lively Debate ◽  
Qubit Operations ◽  
Fundamental Limitation ◽  
Positive Operator Valued Measure

Heisenberg’s uncertainty relations have played an essential role in quantum physics since its very beginning. The uncertainty relations in the modern quantum formalism have become a fundamental limitation on the joint measurements of general quantum mechanical observables, going much beyond the original discussion of the trade-off between knowing a particle’s position and momentum. Recently, the uncertainty relations have generated a considerable amount of lively debate as a result of the new inequalities proposed as extensions of the original uncertainty relations. We report an experimental test of one of the new Heisenberg’s uncertainty relations using a single 40Ca+ ion trapped in a harmonic potential. By performing unitary operations under carrier transitions, we verify the uncertainty relation proposed by Busch, Lahti, and Werner (BLW) based on a general error–trade-off relation for joint measurements on two compatible observables. The positive operator-valued measure, required by the compatible observables, is constructed by single-qubit operations, and the lower bound of the uncertainty, as observed, is satisfied in a state-independent manner. Our results provide the first evidence confirming the BLW-formulated uncertainty at a single-spin level and will stimulate broad interests in various fields associated with quantum mechanics.

scholarly journals On Uncertainty Relations and Entanglement Detection with Mutually Unbiased Measurements

2015 ◽  
Vol 22 (01) ◽  
pp. 1550005 ◽  
Author(s):  
Alexey E. Rastegin
Keyword(s):  
The State ◽  
Uncertainty Relations ◽  
Trade Off ◽  
Entropic Uncertainty Relations ◽  
Finite Dimensional ◽  
State Dependent ◽  
Entanglement Detection

We formulate some properties of a set of several mutually unbiased measurements. These properties are used for deriving entropic uncertainty relations. Applications of mutually unbiased measurements in entanglement detection are also revisited. First, we estimate from above the sum of the indices of coincidence for several mutually unbiased measurements. Further, we derive entropic uncertainty relations in terms of the Rényi and Tsallis entropies. Both the state-dependent and state-independent formulations are obtained. Using the two sets of local mutually unbiased measurements, a method of entanglement detection in bipartite finite-dimensional systems may be realized. A certain trade-off between a sensitivity of the scheme and its experimental complexity is discussed.

Uncertainty relations expressed by Shannon-like entropies

Open Physics ◽  
2003 ◽  
Vol 1 (3) ◽  
Author(s):  
V. Majerník ◽  
Eva Majerníková ◽  
S. Shpyrko
Keyword(s):  
Shannon Entropy ◽  
Uncertainty Principle ◽  
Quantum Physics ◽  
Graphical Representations ◽  
Uncertainty Relations ◽  
Entropic Uncertainty Relations

AbstractBesides the well-known Shannon entropy, there is a set of Shannon-like entropies which have applications in statistical and quantum physics. These entropies are functions of certain parameters and converge toward Shannon entropy when these parameters approach the value 1. We describe briefly the most important Shannon-like entropies and present their graphical representations. Their graphs look almost identical, though by superimposing them it appears that they are distinct and characteristic of each Shannon-like entropy. We try to formulate the alternative entropic uncertainty relations by means of the Shannon-like entropies and show that all of them equally well express the uncertainty principle of quantum physics.

REALISTIC SIMULATIONS OF SINGLE-SPIN MEASUREMENT VIA MAGNETIC RESONANCE FORCE MICROSCOPY

2005 ◽  
Vol 03 (supp01) ◽  
pp. 1-9 ◽  
Author(s):  
TODD A. BRUN ◽  
HSI-SHENG GOAN
Keyword(s):  
Magnetic Resonance ◽  
Thermal Noise ◽  
Quantum Information Processing ◽  
Nuclear Spins ◽  
Magnetic Resonance Force Microscopy ◽  
Force Microscopy ◽  
Single Spin ◽  
Structure Of Molecules ◽  
Spin Level ◽  
Back Action

The problem of measuring single electron or nuclear spins is of great interest for a variety of purposes, from imaging the structure of molecules to quantum information processing. One of the most promising techniques is magnetic resonance force microscopy (MRFM), in which the force between a spin and a small permanent magnet resonantly drives the oscillations of a microcantilever. Numerous issues arise in understanding this system: thermal noise in the cantilever, shot-noise and back-action from monitoring the cantilever's motion, spin relaxation, and interaction with higher cantilever modes. Detailed models of these effects allow one to assess their relative importance and the necessary improvements for sensitivity at the single-spin level.

scholarly journals Measurements of Entropic Uncertainty Relations in Neutron Optics

2020 ◽  
Vol 10 (3) ◽  
pp. 1087 ◽  
Author(s):  
Bülent Demirel ◽  
Stephan Sponar ◽  
Yuji Hasegawa
Keyword(s):  
Neutron Spin ◽  
Uncertainty Relations ◽  
Joint Measurement ◽  
Neutron Optics ◽  
First Case ◽  
90Th Anniversary ◽  
Second Category ◽  
Error Correction Procedures ◽  
Projective Measurements ◽  
Positive Operator Valued Measure

The emergence of the uncertainty principle has celebrated its 90th anniversary recently. For this occasion, the latest experimental results of uncertainty relations quantified in terms of Shannon entropies are presented, concentrating only on outcomes in neutron optics. The focus is on the type of measurement uncertainties that describe the inability to obtain the respective individual results from joint measurement statistics. For this purpose, the neutron spin of two non-commuting directions is analyzed. Two sub-categories of measurement uncertainty relations are considered: noise–noise and noise–disturbance uncertainty relations. In the first case, it will be shown that the lowest boundary can be obtained and the uncertainty relations be saturated by implementing a simple positive operator-valued measure (POVM). For the second category, an analysis for projective measurements is made and error correction procedures are presented.

scholarly journals Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 270 ◽  
Author(s):  
Kyunghyun Baek ◽  
Hyunchul Nha ◽  
Wonmin Son
Keyword(s):  
Three Dimensional ◽  
Uncertainty Relations ◽  
Dimensional System ◽  
Direct Sum ◽  
Entropic Uncertainty Relations ◽  
Finite Dimensional ◽  
Uncertainty Bound ◽  
Three Dimensional System ◽  
Unsharp Observables ◽  
Positive Operator Valued Measure

We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our approach provides a significant improvement of the uncertainty bound compared with previous majorization-based approaches (Friendland, S.; Gheorghiu, V.; Gour, G. Phys. Rev. Lett. 2013, 111, 230401; Rastegin, A.E.; Życzkowski, K. J. Phys. A, 2016, 49, 355301), particularly by extending the direct-sum majorization relation first introduced in (Rudnicki, Ł.; Puchała, Z.; Życzkowski, K. Phys. Rev. A 2014, 89, 052115). We illustrate the usefulness of our uncertainty relations by considering a pair of qubit observables in a two-dimensional system and randomly chosen unsharp observables in a three-dimensional system. We also demonstrate that our bound tends to be stronger than the generalized Maassen–Uffink bound with an increase in the unsharpness effect. Furthermore, we extend our approach to the case of multiple POVM measurements, thus making it possible to establish entropic uncertainty relations involving more than two observables.

scholarly journals Zero–trade-off multiparameter quantum estimation via simultaneously saturating multiple Heisenberg uncertainty relations

2021 ◽  
Vol 7 (1) ◽  
pp. eabd2986
Author(s):  
Zhibo Hou ◽  
Jun-Feng Tang ◽  
Hongzhen Chen ◽  
Haidong Yuan ◽  
Gou-Yong Xiang ◽  
...  
Keyword(s):  
Uncertainty Relation ◽  
Uncertainty Relations ◽  
Quantum Metrology ◽  
Trade Off ◽  
Practical Applications ◽  
Multiple Parameters ◽  
Classical Scheme ◽  
Precision Limit ◽  
Heisenberg Uncertainty ◽  
Heisenberg Uncertainty Relations

Quantum estimation of a single parameter has been studied extensively. Practical applications, however, typically involve multiple parameters, for which the ultimate precision is much less understood. Here, by relating the precision limit directly to the Heisenberg uncertainty relation, we show that to achieve the highest precisions for multiple parameters at the same time requires the saturation of multiple Heisenberg uncertainty relations simultaneously. Guided by this insight, we experimentally demonstrate an optimally controlled multipass scheme, which saturates three Heisenberg uncertainty relations simultaneously and achieves the highest precisions for the estimation of all three parameters in SU(2) operators. With eight controls, we achieve a 13.27-dB improvement in terms of the variance (6.63 dB for the SD) over the classical scheme with the same loss. As an experiment demonstrating the simultaneous achievement of the ultimate precisions for multiple parameters, our work marks an important step in multiparameter quantum metrology with wide implications.

scholarly journals La doppia natura dei suicidi del canto XIII dell’Inferno: un parallelismo con la dualità onda-particella nella fisica quantistica

2021 ◽  
pp. 001458582110226
Author(s):  
Simone Raffaello Pengue
Keyword(s):  
Quantum Physics ◽  
Analytical Tool ◽  
Multisensory Interaction ◽  
Hybrid Nature ◽  
Wave Particle Duality ◽  
Lively Debate ◽  
The City ◽  
Peculiar Phenomenon

The hybrid nature of the human–plant suicidal souls explored through the character of Pier delle Vigne in Inferno XIII exhibits unique characteristics in the Comedy’s first cantica. For centuries the Wood of the Suicides has demanded the attention of readers and scholars alike and yet the interplay and structure of their coexisting identities remain subject to lively debate. As an analytical tool, Dante’s encounter with Pier delle Vigne is compared to the wave–particle duality of light, a peculiar phenomenon of quantum physics. Indeed just as the suicides are at once true human and true plant, light behaves simultaneously as wave and particle depending on the experiment performed. The two complementary descriptions of light are mirrored in the duality of Pier delle Vigne, allowing a schematic restating of the canto emphasizing the multisensory interaction between Dante and the sinner. The hybrid nature of the damned soul thus becomes an expression of the contrasting judgments of Dante–theologian and Dante–poet on this character. Furthermore, the analogy shows how the anonymous suicide from Florence introduced at the end of the canto embodies the ambivalent perspective of Dante on the city of Florence itself.

scholarly journals Renyi and Tsallis formulations of noise-disturbance trade-off relations

2016 ◽  
Vol 16 (3&4) ◽  
pp. 313-331
Author(s):  
Alexey E. Rastegin
Keyword(s):  
Probability Distributions ◽  
Conditional Entropy ◽  
Uncertainty Relations ◽  
Theoretic Approach ◽  
Trade Off ◽  
Information Theoretic ◽  
Entropic Uncertainty Relations ◽  
Related Information ◽  
Information Theoretic Measures ◽  
Information Theoretic Approach

We address an information-theoretic approach to noise and disturbance in quantum measurements. Properties of corresponding probability distributions are characterized by means of both the R´enyi and Tsallis entropies. Related information-theoretic measures of noise and disturbance are introduced. These definitions are based on the concept of conditional entropy. To motivate introduced measures, some important properties of the conditional R´enyi and Tsallis entropies are discussed. There exist several formulations of entropic uncertainty relations for a pair of observables. Trade-off relations for noise and disturbance are derived on the base of known formulations of such a kind.

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